I lean towards Intel, because through the years, I tend to think Intel'satech support is better - not calling them, just reading the site and it's resources. I've had a couple of desktops - and one laptop with an AMD processor, with no problems, though.
I don't currently own a laptop. If I did, my usage would be similar to yours. I have an Acer monitor purchased a month or so ago - so far, so good. And an old Gateway 366MHz Celeron tower purchased new in 1997, that soldiers on as a spare.
Of course, that's an eternity, and much has changed - that the fact that that old girl still runs is pretty much meaningless.
Are you planning on this laptop to be your main computer? If so, I'd buy one of those cooling devices, and if portability is a factor that matters, I'd spend some time searching about either products' battery life, and check out to see if there is a big $$ difference if a batt. replacement becomes necessary.
I did read - a year or so ago - that Acer loads a software suite onto their laptops that some folks found objectionable. That might be the case with a Gateway - dunno. Either way, that might be just me - I like a system as clean as possible, and for many, the pre-loaded stuff works out just fine.
You don't seem to be in the market for an earth-shattering system, more to purchasing a main-stream item, so my guess is that you will be happy with either choice.
The usual things apply, desktop vs. laptop...a HW problem that can get fixed for 50 bucks, a hundred bucks on a desktop can run considerably more on a laptop.